KANs with learnable univariate spline activations on edges achieve better accuracy than MLPs with fewer parameters, faster scaling, and direct visualization for scientific discovery.
Representation properties of networks: Kolmogorov’s theorem is irrelevant
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Explicit C2-smooth approximate Kolmogorov superpositions are constructed via translated dilated inner functions and piecewise C2 outer interpolation, achieving N^{-alpha} accuracy for alpha-Holder functions.
P1-KAN introduces a new KAN architecture with theoretical approximation guarantees that outperforms MLPs and prior KAN variants on irregular functions while matching spline KAN accuracy on smooth ones, demonstrated on hydraulic optimization.
citing papers explorer
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KAN: Kolmogorov-Arnold Networks
KANs with learnable univariate spline activations on edges achieve better accuracy than MLPs with fewer parameters, faster scaling, and direct visualization for scientific discovery.
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Explicit Construction of Approximate Kolmogorov Superpositions with C2 Smoothness
Explicit C2-smooth approximate Kolmogorov superpositions are constructed via translated dilated inner functions and piecewise C2 outer interpolation, achieving N^{-alpha} accuracy for alpha-Holder functions.
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P1-KAN: an effective Kolmogorov-Arnold network with application to hydraulic valley optimization
P1-KAN introduces a new KAN architecture with theoretical approximation guarantees that outperforms MLPs and prior KAN variants on irregular functions while matching spline KAN accuracy on smooth ones, demonstrated on hydraulic optimization.